Details

Time bar (total: 13.0s)

sample34.0ms

Algorithm
intervals
Results
15.0ms256×body80valid

simplify1.1s

Counts
1 → 1
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
02937
16230
215430
350230
4176630
done500030

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 24.9b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
0.1b
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
0.3b
(/ (- x 2.0) (/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)))
24.2b
(/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
128×times-frac
96×add-sqr-sqrt *-un-lft-identity
68×add-cube-cbrt
16×associate-/r*
14×distribute-lft-out-- difference-of-squares
11×add-exp-log add-cbrt-cube
8×div-inv associate-/l*
4×pow1 cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u add-log-exp
2×frac-2neg clear-num fma-udef associate-/l/
1×flip3-- div-sub associate-/r/ flip--
Counts
4 → 152
Calls
4 calls:
0.0ms
(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
0.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
24.0ms
(/ (- x 2.0) (/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)))
6.0ms
(/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))

series568.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
27.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
307.0ms
(/ (- x 2.0) (/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)))
197.0ms
(/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))

simplify944.0ms

Counts
164 → 164
Iterations

Useful iterations: done (935.0ms)

IterNodesCost
02667066
16596938
221356594
done50006585

prune817.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
0.2b
(* (/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)) (+ x 2.0))
15.8b
(/ (- (* x x) (* 2.0 2.0)) (* (/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)) (+ x 2.0)))
24.2b
(/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
24×*-un-lft-identity
23×times-frac
22×add-cube-cbrt
20×add-exp-log add-cbrt-cube
13×associate-*l*
7×associate-/l*
6×pow1 cbrt-undiv div-exp
5×associate-/r/
4×expm1-log1p-u frac-times flip3-+ associate-*r/ associate-*r* prod-exp associate-/r* cbrt-unprod flip-+ log1p-expm1-u add-log-exp
3×div-inv
2×frac-2neg associate-*l/ clear-num associate-/l/ difference-of-squares unswap-sqr
1×distribute-rgt-in flip3-- distribute-lft-in div-sub pow-prod-down *-commutative flip-- fma-udef distribute-lft-out
Counts
4 → 115
Calls
4 calls:
0.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
30.0ms
(* (/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)) (+ x 2.0))
29.0ms
(/ (- (* x x) (* 2.0 2.0)) (* (/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)) (+ x 2.0)))
5.0ms
(/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))

series775.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
220.0ms
(* (/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)) (+ x 2.0))
342.0ms
(/ (- (* x x) (* 2.0 2.0)) (* (/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)) (+ x 2.0)))
185.0ms
(/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))

simplify1.2s

Counts
127 → 127
Iterations

Useful iterations: done (1.2s)

IterNodesCost
02114662
16284620
224494005
done50004004

prune599.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

15.8b
(/ (- (* x x) (* 2.0 2.0)) (* (/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)) (+ x 2.0)))
24.2b
(/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))
24.2b
(/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))
24.2b
(/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
31×times-frac
30×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
19×add-exp-log add-cbrt-cube
13×associate-/l*
10×associate-/r*
7×cbrt-undiv div-exp
5×associate-/r/
4×pow1 expm1-log1p-u frac-2neg clear-num log1p-expm1-u div-inv add-log-exp
2×frac-times flip3-+ associate-*r/ prod-exp cbrt-unprod flip-+ associate-/l/ difference-of-squares
1×flip3-- div-sub associate-*l/ flip--
Counts
4 → 122
Calls
4 calls:
31.0ms
(/ (- (* x x) (* 2.0 2.0)) (* (/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)) (+ x 2.0)))
5.0ms
(/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))
5.0ms
(/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))
5.0ms
(/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))

series898.0ms

Counts
4 → 12
Calls
4 calls:
346.0ms
(/ (- (* x x) (* 2.0 2.0)) (* (/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)) (+ x 2.0)))
188.0ms
(/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))
184.0ms
(/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))
179.0ms
(/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))

simplify803.0ms

Counts
134 → 134
Iterations

Useful iterations: done (796.0ms)

IterNodesCost
01635301
14505257
219314636
done50014487

prune857.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

14.2b
(cbrt (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))
14.2b
(cbrt (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))
16.2b
(/ (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (cbrt (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)))
19.4b
(/ (* (cbrt (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)) (cbrt (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
42×times-frac
38×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
27×cbrt-prod sqrt-prod
12×associate-/r*
11×add-exp-log
8×add-cbrt-cube
7×associate-/l*
4×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-undiv div-exp
2×frac-2neg pow1/3 clear-num div-inv
1×prod-exp cbrt-unprod
Counts
4 → 117
Calls
4 calls:
1.0ms
(cbrt (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))
1.0ms
(cbrt (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))
8.0ms
(/ (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (cbrt (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)))
12.0ms
(/ (* (cbrt (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)) (cbrt (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))

series1.3s

Counts
4 → 12
Calls
4 calls:
224.0ms
(cbrt (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))
217.0ms
(cbrt (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))
437.0ms
(/ (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (cbrt (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)))
457.0ms
(/ (* (cbrt (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)) (cbrt (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))

simplify815.0ms

Counts
129 → 129
Iterations

Useful iterations: done (807.0ms)

IterNodesCost
02905745
16445449
218075111
done50004927

prune696.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.0b

regimes344.0ms

Accuracy

96.7% (0.8b remaining)

Error of 0.9b against oracle of 0.0b and baseline of 24.8b

bsearch227.0ms

Steps
ItersRangePoint
8
1.0087090481069135e+28
4.775882038212059e+32
2.198533680668519e+32
9
-2.4158391227535656e+51
-3.837036292109216e+45
-7.689434859723143e+48

simplify6.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
04165
16056
done6056

end0.0ms

sample737.0ms

Algorithm
intervals
Results
489.0ms8008×body80valid